Low loss, frequency selective electrical signal filters for communications applications were developed beginning around 1910, for telegraphy and telephony uses, particularly for multiplexing and de-multiplexing of communication signal channels carried on long distance cables and wireless links. Filter design methods, named “image” or “image parameter” design methods, were developed by Bell Laboratories, among others (see George A. Campbell, “Physical Theory of the Electric Wave Filter”, The Bell System Technical Journal, Volume I, No. 2 (November 1922); Otto J. Zobel, “Theory and Design of Uniform and Composite Electric Wave-Filters”, The Bell System Technical Journal, Volume II, No. 1 (January 1923)). These filter circuits utilized circuit elements, including inductors, capacitors, and transformers.
In the 1920s, Acoustic Wave (AW) resonators, specifically quartz bulk acoustic wave (BAW) resonators, began to be used in some electrical signal filters. The equivalent circuit of an AW resonator has two resonances closely spaced in frequency called the “resonance” frequency and the “anti-resonance” frequency (see K. S. Van Dyke, “Piezo-Electric Resonator and its Equivalent Network” Proc. IRE, Vol. 16, 1928, pp. 742-764). The image filter design methods were applied to filter circuits utilizing these quartz resonators, and two AW filter circuit types resulted: “ladder” and “lattice” AW filter designs (see L. Espenschied, Electrical Wave Filter, U.S. Pat. No. 1,795,204; and W. P. Mason, “Electrical Wave Filters Employing Quartz Crystals as Elements”, The Bell System Technical Journal (1934)).
In the 1920s and 1930s, another approach, which came to be referred to as “network synthesis,” was developed for the design of frequency selective electrical signal filters for communications applications. This new filter circuit design method was pioneered by Foster and Darlington in the United States (see Ronald M. Foster, “A Reactance Theorem,” Bell Syst. Tech. J., Vol 3, 1924, pp. 259-267, and S. Darlington, “Synthesis of Reactance 4-poles which produce prescribed insertion loss characteristics”, J. Math Phys, Vol 18, 1939, pp. 257-353) and Cauer in Germany (see W. Cauer, U.S. Pat. No. 1,989,545; 1935) among others.
In “network synthesis,” after an initial circuit structure is chosen, which includes circuit element types and the way they are interconnected, the desired loss-less filter response is translated into a ratio of complex polynomials in the form of complex frequency dependent circuit response parameters such as scattering parameters, e.g. S21 and S11. The S21 scattering parameter may be represented as follows:
                                          H            ⁡                          (              s              )                                =                                                    N                ⁡                                  (                  s                  )                                                            D                ⁡                                  (                  s                  )                                                      =                          K              ⁢                                                                                                        ⁢                                                            (                                              s                        -                                                  z                          1                                                                    )                                        ⁢                                          (                                              s                        -                                                  z                          2                                                                    )                                        ⁢                                                                                  ⁢                    ⋯                    ⁢                                                                                  ⁢                                          (                                              s                        -                                                  z                                                      m                            -                            1                                                                                              )                                        ⁢                                          (                                              s                        -                                                  z                          m                                                                    )                                                                                                            (                                          s                      -                                              p                        1                                                              )                                    ⁢                                      (                                          s                      -                                              p                        2                                                              )                                    ⁢                                                                          ⁢                  ⋯                  ⁢                                                                          ⁢                                      (                                          s                      -                                              p                                                  n                          -                          1                                                                                      )                                    ⁢                                      (                                          s                      -                                              p                        n                                                              )                                                                                      ,                            [        1        ]            where N(s) is the numerator polynomial, D(s) is the denominator polynomial, the zi's are the roots (or transmission zeroes) of the equation N(s)=0, the pi's are the roots (or reflection zeroes) of the equation D(s)=0, m is the number of transmission zeroes, n is the number of reflection zeroes, and K is a scale factor. (Note: transmission zeroes are the zeroes of S21 and reflection zeroes are the zeroes of S11, for the loss-less case. When the small but finite real losses are added later in the circuit design process these zeroes may become small but no longer precisely zero, and correspond to the natural frequencies, resonances, of the final filter.) The filter circuit element values may then be “synthesized” (calculated) exactly in the loss-less case from the ratio of complex polynomials. Neglecting losses, which are kept small in practice, the response of the “synthesized” circuit matches the desired response function.
In the 1950s and 1960s, network synthesis was successfully applied to the design of microwave filters for communications and other applications. These new filters utilize high Q (low loss) electromagnetic resonators and electromagnetic couplings between these resonators as circuit elements (see George L. Matthaei et al., Microwave Filters, Impedance-Matching Networks, and Coupling Structures, McGraw-Hill Book Company, pp. 95-97, 438-440 (1964); and Richard J. Cameron et al., Microwave Filters for Communication Systems: Fundamentals, Design and Applications, Wiley-Interscience (2007).). Network synthesis was also applied to the design of acoustic wave filters for communications and other applications beginning in the 1960's. (See Anatol I. Zverev, Handbook of Filter Synthesis, John Wiley & Sons, pp. 414-498 (1967); and Robert G. Kinsman, Crystal Filters: Design, Manufacture, and Application, John Wiley & Sons, pp. 37-105 and 117-155, (1987)). In this work, only the resonance of the acoustic wave resonator is included in the initial circuit structure. The anti-resonance is treated as a parasitic effect added into the circuit after the element values of the initial circuit are calculated by the network synthesis method.
Beginning in about 1992, thin film surface acoustic wave (SAW) resonators and thin film BAW resonators were developed and began to be used at microwave frequencies (>500 MHz). AW impedance element filter (IEF) designs, were utilized which is an example of an Espenschied-type ladder acoustic wave filter design (see O. Ikata, et al., “Development of Low-Loss Bandpass Filters Using Saw Resonators for Portable Telephones”, 1992 Ultrasonics Symposium, pp. 111-115; and Ken-ya Hashimoto, Surface Acoustic Wave Devices in Telecommunications: Modeling and Simulation, Springer (2000), pp. 149-161). Image designed AW IEF bandpass filters in SAW and BAW implementations are often used for microwave filtering applications in the radio frequency (RF) front end of mobile communications devices. Of most particular importance in the mobile communication industry is the frequency range from approximately 500-3,500 MHz. In the United States, there are a number of standard bands used for cellular communications. These include Band 2 (˜1800-1900 MHz), Band 4 (˜1700-2100 MHz), Band 5 (˜800-900 MHz), Band 13 (˜700-800 MHz), and Band 17 (˜700-800 MHz); with other bands emerging.
The duplexer, a specialized kind of filter, is a key component in the front end of mobile devices. Modern mobile communications devices transmit and receive at the same time (using Code Division Multiple Access (CDMA), Wide-Band Code Division Multiple Access (WCDMA), or Long Term Evolution (LTE)) and use the same antenna. The duplexer separates the transmit signal, which can be up to 0.5 Watt power, from the receive signal, which can be as low as a pico-Watt. The transmit and receive signals are modulated on carriers at different frequencies allowing the duplexer to select them; even so the duplexer must provide low insertion loss, high selectively, small circuit area, high power handling, high linearity, and low cost. The image designed bandpass AW IEF filter is universally preferred to be used in a duplexer, because it satisfies these requirements, and significantly better than alternatives like the tapped delay line (since it has higher loss), and the resonant single-phase unidirectional transducer (SPUDT) filter (since the narrow lines required prevent scaling to microwave frequencies); although the double-mode SAW (DMS) (also called longitudinally coupled resonator (LCR)) filter is sometimes used for the receive filter in a duplexer due to the balanced output it provides and improved rejection. (See David Morgan, Surface Acoustic Wave Filters With Applications to Electronic Communications and Signal Processing, pp. 335-339, 352-354 (2007)).
Minor variations to these traditional AW IEF filter designs have also been considered for these applications (see, for example, U.S. Pat. Nos. 8,026,776 and 8,063,717), which typically add one or more circuit elements (e.g. capacitor, inductor, or AW resonator) to the IEF design to enhance or add a particular circuit feature. This can be accomplished when the influences to the AW IEF circuit are minor enough that currently used computer optimization tools converge and produce an improved design after the additional element(s) are added, as compared to the optimized IEF. This is a stringent requirement for any circuit containing AW resonators, with their closely spaced resonances and anti-resonances, and thus permits only very minor variations to the basic AW IEF design and function.
There is a need for improved microwave acoustic wave filters to provide improved performance, smaller size, and lower cost; as well as to incorporate tunability. Network synthesis offers a path when the compound nature of the acoustic wave resonator is incorporated directly into the network synthesis process—the subject of this invention.